Logarithmic singularity

This paper is a continuation of Fefferman’s program [7] for studying the geometry and analysis of strictly pseudoconvex domains. The key idea of the program is to consider the Bergman and Szeg¨ kernels of the domains as o analogs of the heat kernel of Riemannian manifolds. In Riemannian (or conformal) geometry, the coefficients of the asymptotic expansion of the heat kernel can be expressed in terms of the curvature of the metric; by integrating the coefficients one obtains index theorems in various settings. ...

18p noel_noel 17-01-2013 50 5   Download

We verify an old conjecture of G. P´lya and G. Szeg˝ saying that the o o regular n-gon minimizes the logarithmic capacity among all n-gons with a fixed area. 1. Introduction The logarithmic capacity cap E of a compact set E in R2 , which we identify with the complex plane C, is defined by (1.1) − log cap E = lim (g(z, ∞) − log |z|), z→∞ where g(z, ∞) denotes the Green function of a connected component Ω(E) ∞ of C \ E having singularity at z = ∞; see [4, Ch. 7], [7, §11.1]. By an n-gon with...

28p tuanloccuoi 04-01-2013 60 9   Download